Inference for Misspecified Models With Fixed Regressors

By Alberto Abadie, Guido W. Imbens, Fanyin Zheng. 2014

50 citations recorded by the source corpus.

Following the work by Eicker, Huber, and White it is common in empirical work to report standard errors that are robust against general misspecification. In a regression setting, these standard errors are valid for the parameter that minimizes the squared difference between the conditional expectation and a linear approximation, averaged over the population distribution of the covariates. Here, we discuss an alternative parameter that corresponds to the approximation to the conditional expectation based on minimization of the squared difference averaged over the sample, rather than the population, distribution of the covariates. We argue that in some cases this may be a more interesting parameter. We derive the asymptotic variance for this parameter, which is generally smaller than the Eicker–Huber–White robust variance, and propose a consistent estimator for this asymptotic variance. Supplementary materials for this article are available online.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6d0ef881e0b5af17778c274dce4019c3703f2188

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Citations in the corpus

Inference in Linear Regression Models with Many Covariates and Heteroscedasticity (2015, background): “…and White 1985; Wu 1986; Chesher and Jewitt 1987; Shao and Wu 1987; Chesher 1989; Cribari-Neto, Ferrari, and Cordeiro 2000; Kauermann and Carroll 2001; Bera, Suprayitno, and Premaratne 2002; Stock and Watson 2008; Cribari-Neto, da Gloria, and Lima 2011; Müller 2013; Abadie, Imbens, and Zheng 2014).”
Revisiting event study designs: robust and efficient estimation (2021, methodology): “With this approach, we follow Abadie et al. (2014) in focussing on an in-sample estimand, which in our case is a weighted sample average treatment effect for those observations that were actually treated.”
Simple and honest confidence intervals in nonparametric regression (2016, methodology): “For inference at a point and sharp RD, the estimator T̂ (ĥ∗rmse; k) is a weighted least squares estimator, and one can directly estimate its finite-sample conditional variance by the nearest neighbor variance estimator considered in Abadie and Imbens (2006) and Abadie et al. (2014).”
Inference in Regression Discontinuity Designs with a Discrete Running Variable (2016, methodology): “To explain the construction, let τ̃h = E(τ̂ | X1, . . . , XNh) denote conditional expectation of the treatment effect estimator, and let σ̂2NN/Nh denote the nearest-neighbor estimator (Abadie and Imbens, 2006; Abadie et al., 2014) of V(τ̂ | X1, . . . , XNh), the conditional variance of τ̂ .”